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Elementary matrices

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A nonsingular matrix can be written as a product of elementary matrices.
Row operations are given by multiplication by elementary matrices.
Elementary matrices are invertible/nonsingular.
Definition of elementary matrix

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A nonsingular matrix can be written as a product of elementary matrices.

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Equivalence theorem for nonsingular matrices: the matrix A row-reduces to the identity matrix.Close match
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Equivalence theorem for nonsingular matrices: the matrix A is a change-of-basis matrix.Close match
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